Question

A cylindrical block of mass M=50kg and height h=0.2m is hanging on a rope and is in equilibrium. Any difference in atmospheric pressure along the height of the block is negligible. What is the tension of the rope in N? For gravity use approximate round value g = 10 m/s²

1) 500

The cylindrical block of mass M=50kg and height h=0.2m is hanging on a rope and is in equilibrium. The cylindrical block is fully immersed in water with density ρ=1000 kg/m³ remaining suspended by the rope and in equilibrium. The top of the cylinder is at the surface level. What is the difference of pressure in the bottom to the pressure from the top? Write into the answer the numerical part of the value of the pressure difference if the unit of measurement for pressure is Pascal. For gravity use approximate round value g = 10 m/s².

2) 2,000

Mentioned above cylindrical block is made from the material with the density ρₛ=2000 kg/m³. What is the tension of the rope when the cylinder is in the condition of question 2? Write into the answer the numerical part of the value of the tension if the unit of measurement for tension is Newton. For gravity use approximate round value g = 10 m/s².

3) 250

I understand the rest and answered it above ^. I'm having trouble with question 4.

QUESTION 4: If the top of the cylindrical block is immersed further to a depth of 1m, what is now the tension of the rope?

PLEASE SHOW YOUR CALCULATION WORK.

Answer 1

Note that buoyancy force does not depend on where the block is. It only depends on the volume of solid submerged in the liquid. Since the volume submerged is the same in parts 3/4, the answer to tension comes out to be same in both the cases.